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Measurement-Based and Universal Blind Quantum Computation

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Formal Methods for Quantitative Aspects of Programming Languages (SFM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6154))

Abstract

Measurement-based quantum computation (MBQC) is a novel approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operation. We review here the mathematical model underlying MBQC and the first quantum cryptographic protocol designed using the unique features of MBQC.

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References

  1. Anders, J., Browne, D.E.: Computational power of correlations. Physical Review Letters 102, 050502 (4 pages) (2009)

    Google Scholar 

  2. Aharonov, D., Ben-Or, M., Eban, E.: Interactive proofs for quantum computations. In: Proceedings of Innovations in Computer Science (ICS 2010), pp. 453–469 (2010)

    Google Scholar 

  3. Abadi, M., Feigenbaum, J., Kilian, J.: On hiding information from an oracle. Journal of Computer and System Sciences 39, 21–50 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Aharonov, D., Jones, V., Landau, Z.: A polynomial quantum algorithm for approximating the Jones polynomial. In: Proceedings of the 38th annual ACM symposium on Theory of computing (STOC 2006), pp. 427–436 (2006)

    Google Scholar 

  5. Aliferis, P., Leung, D.W.: Simple proof of fault tolerance in the graph-state model. Phys. Rev. A 73 (2006)

    Google Scholar 

  6. Ambainis, A., Mosca, M., Tapp, A., de Wolf, R.: Private quantum channels. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS 2000), pp. 547–553 (2000)

    Google Scholar 

  7. Arrighi, P., Salvail, L.: Blind quantum computation. International Journal of Quantum Information 4, 883–898 (2006)

    Article  MATH  Google Scholar 

  8. Barendregt, H.P.: The Lambda Calculus, Its Syntax and Semantics. In: Studies in Logic. North-Holland, Amsterdam (1984)

    Google Scholar 

  9. Brassard, G., Bennett, C.H.: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (1984)

    Google Scholar 

  10. Browne, D.E., Briegel, H.J.: One-way quantum computation. In: Lectures on Quantum Information, pp. 359–380. Wiley-VCH, Berlin (2006)

    Chapter  Google Scholar 

  11. Barnum, H., Crépeau, C., Gottesman, D., Smith, A., Tapp, A.: Authentication of quantum messages. In: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2002), p. 449 (2002)

    Google Scholar 

  12. Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation. In: Proceedings of the 50th Annual Symposium on Foundations of Computer Science (FOCS 2009), pp. 517–527 (2009)

    Google Scholar 

  13. Broadbent, A., Kashefi, E.: Parallelizing quantum circuits. In: Theoretical Computer Science, pp. 2489–2510 (2009)

    Google Scholar 

  14. Browne, D., Kashefi, E., Mhalla, M., Perdrix, S.: Generalized flow and determinism in measurement-based quantum computation. New Journal of Physics 9 (2007)

    Google Scholar 

  15. Boykin, P.O., Roychowdhury, V.: Optimal encryption of quantum bits. Physical Review A 67, 042317 (2003)

    Article  Google Scholar 

  16. Bernstein, E., Vazirani, U.: Quantum complexity theory. SIAM Journal of Computing 5(26) (1997)

    Google Scholar 

  17. Childs, A.M.: Secure assisted quantum computation. Quantum Information and Computation 5, 456–466 (2005); Initial version appeared online in (2001)

    MathSciNet  MATH  Google Scholar 

  18. Choi, M.D.: Completely positive linear maps on complex matrices. Linear Algebra and Applications 10 (1975)

    Google Scholar 

  19. Childs, A.M., Leung, D.W., Nielsen, M.A.: Unified derivations of measurement-based schemes for quantum computation. Physical Review A 71 (2005), quant-ph/0404132

    Google Scholar 

  20. Childs, A.M., Leung, D.W., Nielsen, M.A.: Unified derivations of measurement-based schemes for quantum computation. Physical Review A 71, 032318 (14 pages) (2005)

    Google Scholar 

  21. Dür, W., Aschauer, H., Briegel, H.J.: Multiparticle entanglement purification for graph state. Physical Review Letters 91 (2003), quant-ph/0303087

    Google Scholar 

  22. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London A400 (1985)

    Google Scholar 

  23. Deutsch, D.: Quantum computational networks. Proc. Roy. Soc. Lond A 425 (1989)

    Google Scholar 

  24. Danos, V., Kashefi, E.: Determinism in the one-way model. Physical Review A 74, 052310 (6 pages) (2006)

    Google Scholar 

  25. Danos, V., Kashefi, E., Panangaden, P.: Parsimonious and robust realizations of unitary maps in the one-way model. Physical Review A 72 (2005)

    Google Scholar 

  26. Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. Journal of ACM 54, 8 (45 pages) (2007)

    Google Scholar 

  27. Dürr, C., Santha, M.: A decision procedure for unitary linear quantum cellular automata. In: Proceedings of FOCS 1996 – Symposium on Foundations of Computer Science, LNCS. Springer, Heidelberg (1996), quant-ph/9604007

    Google Scholar 

  28. Feigenbaum, J.: Encrypting problem instances: Or... can you take advantage of someone without having to trust him? In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 477–488. Springer, Heidelberg (1986)

    Google Scholar 

  29. Gottesman, D., Chuang, I.L.: Quantum teleportation is a universal computational primitive. Nature 402 (1999)

    Google Scholar 

  30. Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In: Proceedings of the 40th annual ACM symposium on Theory of computing, pp. 113–122 (2008)

    Google Scholar 

  31. Greentree, A.D., Olivero, P., Draganski, M., Trajkov, E., Rabeau, J.R., Reichart, P., Gibson, B.C., Rubanov, S., Huntington, S.T., Jamieson, D.N., Prawer, S.: Critical components for diamond-based quantum coherent devices. Journal of Physics: Condensed Matter 18, 825–842 (2006)

    Google Scholar 

  32. Gottesoman, D.: Stabilizer codes and quantum error correction. PhD thesis, California Institute of Technology (1997)

    Google Scholar 

  33. Gottesman, D.: Fault-tolerant quantum computation with local gates. Journal of Modern Optics 47, 333–345 (2000)

    Article  MathSciNet  Google Scholar 

  34. Hein, M., Eisert, J., Briegel, H.J.: Multi-party entanglement in graph states. Physical Review A 69 (2004)

    Google Scholar 

  35. Kitaev, A.Y.: Quantum computations: algorithms and error correction. Russian Mathematical Surveys 52, 1191–1249 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  36. Knill, E., Laflamme, R.: A theory of quantum error-correcting codes. Physical Review Letters 84, 2525 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  37. Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Physical Review A 78, 042309 (17 pages) (2008)

    Google Scholar 

  38. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  39. Nielsen, M.A., Dawson, C.M.: Fault-tolerant quantum computation with cluster states. Phys. Rev. A 71 (2005)

    Google Scholar 

  40. Nielsen, M.A.: Universal quantum computation using only projective measurement, quantum memory and preparation of the 0 state. Physical Review A 308 (2003)

    Google Scholar 

  41. Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Dordrecht (1995)

    MATH  Google Scholar 

  42. Preskill, J.: Fault-tolerant quantum computation. In: Lo, H.K., Popescu, S., Spiller, T.P. (eds.) Introduction to Quantum Computation and Information. World Scientific, Singapore (1998)

    Google Scholar 

  43. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Physical Review Letters 86 (2001)

    Google Scholar 

  44. Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Physical Review A 68 (2003)

    Google Scholar 

  45. Raussendorf, R., Harrington, J., Goyal, K.: A fault-tolerant one-way quantum computer. Annals of Physics 321, 2242–2270 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  46. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21, 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  47. Selinger, P.: Towards a quantum programming language. Mathematical Structures in Computer Science 14(4) (2004)

    Google Scholar 

  48. Selinger, P. (ed.): Proceedings of the 3nd International Workshop on Quantum Programming Languages. ENTCS (2005)

    Google Scholar 

  49. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26, 1484–1509 (1997); First published in 1995

    Article  MathSciNet  MATH  Google Scholar 

  50. Schumacher, B., Werner, R.F.: Reversible quantum cellular automata (2004), quant-ph/0405174

    Google Scholar 

  51. Unruh, D.: Quantum programs with classical output streams. In: Selinger [Sel05] (2005)

    Google Scholar 

  52. van Dam, W.: Quantum cellular automata. Master’s thesis, Computer Science Nijmegen (1996)

    Google Scholar 

  53. Watrous, J.: On one-dimensional quantum cellular automata. In: Proceedings of FOCS 1995 – Symposium on Foundations of Computer Science, LNCS. Springer, Heidelberg (1995)

    Google Scholar 

  54. Zeng, B., Cross, A., Chuang, I.L.: Transversality versus universality for additive quantum codes (2007), arXiv:0706.1382v3 (quant-ph)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Quantum Computing, University of Waterloo, Canada

    Anne Broadbent & Joseph Fitzsimons

  2. Materials Department, University of Oxford, United Kingdom

    Joseph Fitzsimons

  3. School of Informatics, University of Edinburgh, United Kingdom

    Elham Kashefi

Authors
  1. Anne Broadbent
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  2. Joseph Fitzsimons
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  3. Elham Kashefi
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Fisica e Informatica, Università di Urbino “Carlo Bo”, Piazza della Repubblica 13, 61029, Urbino, Italy

    Alessandro Aldini  & Marco Bernardo  & 

  2. Dipartimento di Informatica, Università di Verona, Ca’ Vignal 2 - Strada le Grazie 15, 37134, Verona, Italy

    Alessandra Di Pierro

  3. Department of Computing, Imperial College London, Huxley Building, 180 Queen’s Gate, SW7 2BZ, London, UK

    Herbert Wiklicky

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Broadbent, A., Fitzsimons, J., Kashefi, E. (2010). Measurement-Based and Universal Blind Quantum Computation. In: Aldini, A., Bernardo, M., Di Pierro, A., Wiklicky, H. (eds) Formal Methods for Quantitative Aspects of Programming Languages. SFM 2010. Lecture Notes in Computer Science, vol 6154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13678-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-13678-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13677-1

  • Online ISBN: 978-3-642-13678-8

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